@csx_intro #T #HLT2 #HT2
elim (cpx_inv_lift1 … HLT2 … HL21 … HT12) -HLT2 #T0 #HT0 #HLT10
@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_mono … HT0 … HT12) in HT2; -T1 /2 width=1 by/
+>(lift_mono … HT0 … HT12) in HT2; -T0 /2 width=1 by/
qed.
(* Basic_1: was just: sn3_gen_lift *)
elim (lift_total T l m) #T0 #HT0
lapply (cpx_lift … HLT2 … HL12 … HT21 … HT0) -HLT2 #HLT10
@(IHT1 … HLT10) // -L1 -L2 #H destruct
->(lift_inj … HT0 … HT21) in HT2; -T1 /2 width=1 by/
+>(lift_inj … HT0 … HT21) in HT2; -T0 /2 width=1 by/
qed.
(* Advanced inversion lemmas ************************************************)